Question

If the axes are rotated through an angle 45°, the coordinates of
(2√2,-3√2) in the new system are
1) (-1, 5) 2) (2,-5) 3) (5, -8)
4) (3,-2)​

Answer 1

Therefore the new coordinate of the given point is (-1,-5).

Step-by-step explanation:

If the coordinate axes are rotated through an angle θ.

Then a point P(x,y) will have co-ordinate P(x',y').

x'= x cosθ+ y sinθ   and  y' =  y cosθ - x sinθ

Given point is  $P(2\sqrt2,-3\sqrt2)$

Then the new coordinate of the point is

$x'= 2\sqrt2 cos 45^\circ+(-3\sqrt2)sin45^\circ$

    $=2\sqrt2\times\frac{1}{\sqrt2} -3\sqrt2\times\frac{1}{\sqrt2}$

    =2-3

    = -1

$y'= -3\sqrt2 cos 45^\circ-2\sqrt2sin45^\circ$

    $=-3\sqrt2\times\frac{1}{\sqrt2} -2\sqrt2\times\frac{1}{\sqrt2}$

   =-3-2

  = -5

Therefore the new coordinate of the given point is (-1,-5).

Answer 2

Answer:

answer-(1,3)

Step-by-step explanation:

plz hi bro I don't time to explain sorry